This explanation is widespread but imprecise. The rule is that the mubtada' of the nominal sentence after these particles must be accusative. This can be a sentence with the noun first (as implied) BUT it can also be a sentence with a khabar muqaddam (a sentence where the predicate comes first because the mubtada' is indefinite). You still make the 'subject' accusative, though, so it would read with case vowels:

Your first sentence would have originally been "انا عندي سيارة" which means "As for me, I have a car" more than just "I have a car". You are setting up a thematic topic rather than using the actual subject of the verbless sentence, which is 'car'. Literally: "at me is a car/a car is at me". Just as 'car' is the subject of 'is' in the literal translation, so also it is the mubtada' in the Arabic - it has just been moved to the end because of its indefiniteness.

The second example you gave is impossible because you definitely can't have a nominative noun (أنا) after an أنّ. Remember that the endings ني، ي are just the accusative and genitive forms of nominative انا.

4. Is the omission of انَّ in the sentence كم أتمنى لو عندي سيارة colloquial or can the same be done in MSA?

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As far as I know, you can't use لو with a verbless sentence - which is why the construction with أنّ exists, in my opinion.

5. Does the use of كم in كم أتمنى لو عندي سيارة simply add emphasis to the sentence? Can it be omitted? Is the use of كم in this sentence applicable to both MSA and colloquial Arabic?

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You know, it literally means 'how much' so you can imagine its force in Arabic. It's not necessary - the rest of the sentence does the semantic work. I don't believe that the exact word كم is used this way in most dialects but I will defer to my Arab colleagues for that one.

Your first sentence would have originally been "انا عندي سيارة" which means "As for me, I have a car" more than just "I have a car". You are setting up a thematic topic rather than using the actual subject of the verbless sentence, which is 'car'. Literally: "at me is a car/a car is at me". Just as 'car' is the subject of 'is' in the literal translation, so also it is the mubtada' in the Arabic - it has just been moved to the end because of its indefiniteness.

It doesn't. I don't know how he arrived at that conclusion. 'As for me' would be أمّا أنا

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I disagree - sorry I didn't see this response earlier. In fact, I should have added the caveat that 'as for me' is only an approximation of what's happening in Arabic. Bear with me please!

The reason I translated it that way was to create an English difference between the following clauses:
لانّ عندي سيّارةً

لأنني عندي سيّارةٌ

Arabic is a thematic/topicalizing language, i.e., you can set up a جملة اسمية with a مبتدا that is not actually the subject of the action in the sentence - so there is, grammatically, and especially in the formally declined language, an important difference between:
يسكن في بيت

هو يسكن في بيت

The first sentence means, literally, "He lives in a house", no?

Then we have to account for the added information with the addition of هو, which is a topic (not a subject) in a جملة اسميّة . To do this, I often translate it as "as for him, he lives in a house" or "him? he lives in a house" because if students remain conscious of this distinction, they will have less trouble with the following pair, which further illustrates my point:
يسكن الطلاب في بيت

الطلاب يسكنون في بيت

Again, we have the same idea, only with 'students' as the subject in the first sentence and the topic in the second. The first sentence is "The students live in a house" whereas the second sentence, though impossible to translate into English, is more like "Them, they live in a house". Something grammatically possible in French and Arabic but not English. This way, the use of the word 'they' in English occurs alongside the usage of the هم form of the verb in Arabic.

This difference is hard to translate and I use "as for..." as a way to make it grammatical in English although I'm aware of امّا. But again, the proof that there is a difference lies in the fact that

1) only the second versions of these sentences can be a complement of انّ
2) the second version require[SIZE=2]s [SIZE=2]that the verb be marked if the subject is plural

[SIZE=2]Lan[SIZE=2]guages like Arabic that topicalize in t[SIZE=2]h[SIZE=2]is [SIZE=2]way al[SIZE=2]so don't often have a developed passive agent system, which is why you can't say

[SIZE=2]"[SIZE=2]The man was killed [B]by[/B] someone" in [SIZE=2]Arabic[SIZE=2], because you have availab[SIZE=2]le structures like
[SIZE=2]
[SIZE=4]الرجل قتله فلانٌ[/SIZE][/SIZE][/SIZE][/SIZE][/SIZE][/SIZE][/SIZE][/SIZE][/SIZE][/SIZE][/SIZE][/SIZE][/SIZE][/SIZE][/SIZE]

Here, the word 'man' is nominative but is only setting up focus for the action whilst the actual subject is 'someone'.

The reason I translated it that way is to render the redundancy. Since عندي سيارة already means "I have a car" the addition of انا is doing something different than the word "I" in English, and I am accounting for that. See my long post for more details.

Also, does مبتدأ mean subject?

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No, it doesn't and it is an important distinction. المبتدأ is the first word in a nominal sentence and gives a topic or theme for what follows (the predicate, called the خبر). Subject in Arabic is فاعل and there are important semantic and usage distinctions between them. By translating "I have a car" and "Me, I have a car/as for me, I have a car" differently, you maintain these distinctions in English, even though you might not do so in an actual translation/interpretation. Sorry for taking so long to get back.

Sorry, I don't think 'as for' is suitable; 'as for' is quite a close equivalent for أمّا هو يسكن في البيت، أمّا عن الطلاب فيسكنون في البيت، etc. Adding a هو to a valid جملة فعلية adds a degree of redundancy but no real meaning for me - except where we want to say 'it's him [not her] who lives ...' which in standard Arabic often uses a بل that is dropped in dialects.
So
يسكن he lives = هو يسكن
أمّا هو فيسكن as for him, he lives
بل هو يسكن أو بل هو الذي يسكن it's actually him who lives

Again, I wasn't offering a translation - only a technique for keeping track of the grammatical distinction between nominal and verbal sentences. I totally understand your personal reaction, but my rendering - while I wouldn't use it in an actual translation of any kind - allows for rigorous typological data to be taken into account in explaining the various differences between these kinds of phrases.

How, for example, would you translate: انا والدي ليس عنيا or any such similar sentences which I've found many of during a cursory search? You either ignore the pronoun or add something that can't always be substituted - and I think 'as for' is as good as anything in this case.